Birth Of A Theorem

Birth of a Theorem
by Cédric Villani

In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani’s own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career.
But you don’t have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn’t simplify or overexplain; rather, it invites readers into collaboration. Villani’s diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You’re privy to the dining-hall conversations at the world’s greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker’s whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.


Birth of a Theorem
by Cedric Villani

âeoeThis man could plainly do for mathematics what Brian Cox has done for physicsâe âe" Sunday Times

How does a genius see the world? Where and how does inspiration strike?

Cédric Villani takes us on a mesmerising adventure as he wrestles with the Boltzmann equation âe" a new theorem that will eventually win him the most coveted prize in mathematics and a place in the mathematical history books. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness.

His story is one of courage and partnership, doubt and anxiety, elation and despair. Of ordinary family life blurring with the abstract world of mathematical physics, of theories and equations that haunt your dreams and seeking the elusive inspiration found only in a locked, darkened room.

Blending science with history, biography with myth, Villani conjures up an inimitable cast: the omnipresent Einstein, mad genius Kurt Godel, and Villaniâe(tm)s personal hero, John Nash.

Step inside the magical world of Cédric Villaniâe¦


Birth of a Theorem
by Cédric Villani

“This man could plainly do for mathematics what Brian Cox has done for physics” Sunday Times

How does a genius see the world? Where and how does inspiration strike?

Cédric Villani takes us on a mesmerising adventure as he wrestles with the Boltzmann equation – a new theorem that will eventually win him the most coveted prize in mathematics and a place in the mathematical history books. Along the way he encounters obstacles and setbacks, losses of faith and even brushes with madness.

His story is one of courage and partnership, doubt and anxiety, elation and despair. Of ordinary family life blurring with the abstract world of mathematical physics, of theories and equations that haunt your dreams and seeking the elusive inspiration found only in a locked, darkened room.

Blending science with history, biography with myth, Villani conjures up an inimitable cast: the omnipresent Einstein, mad genius Kurt Godel, and Villani’s personal hero, John Nash.

Step inside the magical world of Cédric Villani…


Euler’s Gem
by David S. Richeson

Leonhard Euler’s polyhedron formula describes the structure of many objects–from soccer balls and gemstones to Buckminster Fuller’s buildings and giant all-carbon molecules. Yet Euler’s formula is so simple it can be explained to a child. Euler’s Gem tells the illuminating story of this indispensable mathematical idea.

From ancient Greek geometry to today’s cutting-edge research, Euler’s Gem celebrates the discovery of Euler’s beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation VE+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula’s scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler’s formula. Using wonderful examples and numerous illustrations, Richeson presents the formula’s many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.

Filled with a who’s who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem’s development, Euler’s Gem will fascinate every mathematics enthusiast.


Unknown Quantity
by John Derbyshire

Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages — and it promises to be just what his die-hard fans have been waiting for. “Here is the story of algebra.” With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel’s proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics — it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.


Uniformization of Riemann Surfaces
by Henri Paul de Saint-Gervais

In 1907, Paul Koebe and Henri Poincare almost simultaneously proved the uniformization theorem: Every simply connected Riemann surface is isomorphic to the plane, the open unit disc, or the sphere. It took a whole century to get to the point of stating this theorem and providing a convincing proof of it, relying as it did on prior work of Gauss, Riemann, Schwarz, Klein, Poincare, and Koebe, among others. The present book offers an overview of the maturation process of this theorem. The evolution of the uniformization theorem took place in parallel with the emergence of modern algebraic geometry, the creation of complex analysis, the first stirrings of functional analysis, and with the flowering of the theory of differential equations and the birth of topology. The uniformization theorem was, thus, one of the lightning rods of 19th century mathematics. Rather than describe the history of a single theorem, the book aims to return to the original proofs, to look at these through the eyes of modern mathematicians, to inquire as to their correctness, and to attempt to make them rigorous while respecting, as much as possible, the state of mathematical knowledge at the time, or, if this should prove impossible, then to use modern mathematical tools that were not available to the authors of the original proofs. This book will be useful to mathematicians wishing to cast a glance back at the history of their discipline. It should also provide graduate students with a non-standard approach to concepts of great importance for modern research.

Graphs, Colourings and the Four-Colour Theorem
by Robert A. Wilson

The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler’s polyhedral formula, and the first published false `proof’ of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.

Spirals in Time
by Helen Scales

Seashells are the sculpted homes of a remarkable group of animals: the molluscs. These are some of the most ancient and successful animals on the planet.

But watch out. Some molluscs can kill you if you eat them. Some will kill you if you stand too close. That hasn’t stopped people using shells in many ways over thousands of years. They became the first jewelry and oldest currencies; they’ve been used as potent symbols of sex and death, prestige and war, not to mention a nutritious (and tasty) source of food.

Spirals in Time is an exuberant aquatic romp, revealing amazing tales of these undersea marvels. Helen Scales leads us on a journey into their realm, as she goes in search of everything from snails that ‘fly’ underwater on tiny wings to octopuses accused of stealing shells and giant mussels with golden beards that were supposedly the source of Jason’s golden fleece, and learns how shells have been exchanged for human lives, tapped for mind-bending drugs and inspired advances in medical technology. Weaving through these stories are the remarkable animals that build them, creatures with fascinating tales to tell, a myriad of spiralling shells following just a few simple rules of mathematics and evolution.

Shells are also bellwethers of our impact on the natural world. Some species have been overfished, others poisoned by polluted seas; perhaps most worryingly of all, molluscs are expected to fall victim to ocean acidification, a side-effect of climate change that may soon cause shells to simply melt away. But rather than dwelling on what we risk losing, Spirals in Time urges you to ponder how seashells can reconnect us with nature, and heal the rift between ourselves and the living world.


Stonehenge
by Robin Heath

Once part of a large culture of stone circles, Stonehenge�built around 3000 B.C. and developed over the next 1,500 years�is the most famous. The remains of a once-wealthy and evidently learned tribal community, it reflects the apparently disparate subjects of archaeology, astronomy, metrology, sacred geometry, and even shamanism. How were eclipses predicted at Stonehenge? Why were some stones brought all the way from Wales? What is the secret geometry of seven eights? These and many other questions are answered�and Stonehenge’s secrets revealed�in this fascinating small book.


Euclid’s Elements
by Euclid, Dana Densmore

The classic Heath translation, in a completely new layout with plenty of space and generous margins. An affordable but sturdy sewn hardcover student and teacher edition in one volume, with minimal notes and a new index/glossary.


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